Klep and Velu\v{s}\v{c}ek generalized the Krull--Baer theorem for
higher level preorderings to the non-commutative setting. A $n$-real valuation
$v$ on a skew field $D$ induces a group homomorphism $\overline{v}$. A section
of $\overline{v}$ is a crucial ingredient of the construction of a complete
preordering on the base field $D$ such that its projection on the residue skew
field $k_v$ equals the given level $1$ ordering on $k_v$. In the article we give
a proof of the existence of the section of $\overline{v}$, which was left as an
open problem by Klep and Velu\v{s}\v{c}ek, and thus
complete the generalization of the Krull--Baer theorem for preorderings.